{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Single source sand piles\n",
    "\n",
    "An exploration of the single source sand pile model and the fractals it produces.\n",
    "\n",
    "Copyright 2016 Allen Downey, [MIT License](http://opensource.org/licenses/MIT)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "%matplotlib inline\n",
    "%precision 3\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import thinkplot\n",
    "\n",
    "from matplotlib import rc\n",
    "rc('animation', html='html5')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sand pile"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Sand.py` contains an implementation of the sand pile model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from Sand import SandPile, SandPileViewer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`run_ss_pile` initializes a pile with `2**k` grains in the center cell, then runs until equilibrium."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def run_ss_pile(n, k=10):\n",
    "    \"\"\"Runs a single source model.\n",
    "    \n",
    "    k: integer power of two of height\n",
    "    \"\"\"\n",
    "    pile = SandPile(n)\n",
    "    pile.single_source(2**k)\n",
    "    print(pile.run())        \n",
    "    viewer = SandPileViewer(pile)\n",
    "    return pile, viewer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After initialization, the result looks like a fractal, but as far as I know, no one has estimated its fractal dimension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(14244, 4900462)\n",
      "CPU times: user 9.43 s, sys: 4 ms, total: 9.44 s\n",
      "Wall time: 9.43 s\n"
     ]
    },
    {
     "data": {
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5gRQISlpCFkTzkjbGHve+QckWAkPxyImLxnzxS5koRVCZVx3aaEu0lqSCdZNI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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f70bca58f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% time pile, viewer = run_ss_pile(n=131, k=14)\n",
    "viewer.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`draw_four` draws the cells with each of the given values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def draw_four(pile, vals=range(4)):\n",
    "    thinkplot.preplot(rows=2, cols=2)\n",
    "    \n",
    "    for i, val in enumerate(vals):\n",
    "        thinkplot.subplot(i+1)\n",
    "        viewer.draw_array(pile.array==vals[i], vmax=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'll estimate the fractal dimension for each of these patterns separately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6HVYniuwkRHgwqlIUayNyM1FHhAcAAFzatSI8H7zZciNdTGt/31JRFF3XljuC\n3q7He25rZM+j1o6jXpRNfj+I8BzebBEeVbW1R0TgKn1b3mlrLmfTNl7wnTkCIjwAAODSLhnhiY5w\no1Va3t9r696aB9Qyt4y3bHSfIx1I9zieZdk2l1bv3+3rM0Z2EiI85zCiwiaa2/bp95++/HdHpGfm\n3JSWa21t2WXR53jk+Zu1KsuqRXiuOeBJGgc+bgO7ji+n1+ywt8lhPqHdiAaJpX2u7WtLS/jaf3c1\nAfQu4K3n8gIDnYQBz/VEpyIYMfDZ8x/Zdw2u7g3TeHgDnegkq9B4pAUAAC7t2hGeRER6omXrPaPx\naJLulvLuEQ0St+xrz75t3dfafqy2EUxWvkJkJyHCcz2t7Rl6WkS8Iupif6+R6YSGbK/nkZZzTmd+\nFLg3IjwAAODSiPDknEhP6/PTyB3AyCRdu95oLkt0224jvh0mUbWv79Gw60pl5x4iPHMo/f5L71mW\neEn0ljySV+agvDrfpSWHp7TsslTOeaA1ANGgZ0R4AADApRHhKRncmKl2BzCy4d5q3U5ERjZadKox\nvMqyTfu8Mc9oxLavGNlJiPDM4X6/y1yWVzS7w1i1SM+rc5eOjggPAAC4NCI8EY0Rny39ePa4y4pG\nTaKVU3tEo7x9jzYsbKmYIKKzRoRnHm4kd2Nkh9wR3+hzlEd6RuWazoYIDwAAuLS/vHsHTuFj5Pxr\nekbqjNLTCNtOLhpZZiR1d5H2K3r3YY+7dfktouel5ZwT2cEVyN/O6IrHylMCfAieI/czSJ9ZYX1X\nj+xEEOEBAADTI4dni8HVXMuyT9TEy+GJTprZu3zLPu4RLSKiE0cOz/xG5fZQHeTrPUeRLvBEdMrI\n4QEAAJdGDs8Wjbk9EY9clI9eOGndW2Y8t3cCNs/Fu1PYunwuOlv6CER2gLXW3J4j8K4btevhlmXf\nppKr8+Xl431GZ0CEBwAATI8cnj0EcnuiOSveDN9b7nSaZ/htWD4ayYnOPN/ScZmITj9yeK6rtV/X\nOzo1e73C9lp2q0hOzrK8tsfZrMjhAQAAl0aE5xVuNx3B6ZyBXN2tJC0ztLeKRGO8ebui3Zu9u0jy\ndMYiwoNk707NVxSN9HBO+xHhAQAAl0aV1ivc77KS6/bNlzGnqnzyqrVUDs+nP36W0ZOtdw9edKa0\nbW+/5fET2QHe4ozVXIdH9dVbEeEBAADTI4fnXUwlV2/OTiSHZ+/nwi3b3pzTQ0RnV+TwwBOt5gLV\nV+9ADg9WeG9JAAAgAElEQVQAALg0IjxHIXJWWnNh8juId9095N+p1v1+rCNVM3y8jtcgwoNWT7/3\nFIHdYZ7BI1tFoEUEn4jO/ojwAACASyPCc3RO5OcdXUNbuDk7RHIOhQgPtlD/nswU+SlFc2wkJzna\n9fgKiPAAAIBLI8ID4IEID/YwY+QjP6YZjmcWRHgAAMCl0WkZALCrGSMgMx7T7IjwAACA6THgAQAA\n02PAAwAApseABwAATI8BDwAAmB4DHgAAMD0GPAAAYHoMeAAAwPQY8AAAgOkx4AEAANNjwAMAAKbH\ngAcAAEyPAQ8AAJgeAx4AADA9BjwAAGB6DHgAAMD0GPAAAIDpMeABAADTY8ADAACmx4AHAABMjwEP\nAACYHgMeAAAwPQY8AABgegx4AADA9BjwAACA6THgAQAA02PAAwAApseABwAATI8BDwAAmB4DHgAA\nMD0GPAAAYHq3+/2uX7zd9IsApnW/32/v3ocRuIYB16OuX9UBDwAAwAx4pAUAAKbHgAcAAEyPAQ8A\nAJgeAx4AADA9BjwAAGB6DHgAAMD0GPAAAIDpMeABAADTY8ADAACmx4AHAABMjwEPAACYHgMeAAAw\nPQY8AABgegx4AADA9BjwAACA6THgAQAA02PAAwAApseABwAATI8BDwAAmB4DHgAAMD0GPAAAYHoM\neAAAwPQY8AAAgOkx4AEAANNjwAMAAKbHgAcAAEyPAQ8AAJgeAx4AADA9BjwAAGB6DHgAAMD0GPAA\nAIDpMeABAADTY8ADAACmx4AHAABMjwEPAACYHgMeAAAwPQY8AABgegx4AADA9BjwAACA6THgAQAA\n02PAAwAApseABwAATI8BDwAAmB4DHgAAMD0GPAAAYHoMeAAAwPQY8AAAgOkx4AEAANNjwAMAAKb3\nl9qLt9vt/qodAXAc9/v99u59GIFrGHA96vpVHfB8WfBf4/cGwEH923K7/fu7d2IormHAddxuf5Wv\n8UgLAABMjwEPAACYHgMeAAAwPQY8AABgegx4AADA9BjwAACA6THgAQAA02PAAwAApseABwAATI8B\nDwAAmB4DHgAAMD0GPAAAYHoMeAAAwPQY8AAAgOkx4AEAANNjwAMAAKbHgAcAAEyPAQ8AAJgeAx4A\nADA9BjwAAGB6DHgAAMD0GPAAAIDpMeABAADTY8ADAACmx4AHAABMjwEPAACYHgMeAAAwPQY8AABg\negx4AADA9BjwAACA6THgAQAA02PAAwAApseABwAATO8v794BtLnf78uyLMtv3/7w5Q+327Isy/L9\nn7+8a5eqzra/AF5ndX04Iq5Z0yDCAwAApndLI+zii7fb/X7/1wt3B1Hqc/vtux+XZXnv3cj9fl/t\nh93f28ddE47m35bb7d+X+/0+xQfENew9HpGbj+vApz9+Dv33YpZ7p0/pGpr26W9///L3wr4f4bqL\nL263v8rrFxEeAAAwPXJ4DmrrHVIpyvLSfc32o7Sfv348s7fHwR0ScC75b3x1Xfr9p6b/Tr//VXTl\nBRGfT+La84jsVPY9/X+ua8dGhAcAAEyPCM+byOqEj9wWG7G5mb/b/xYbed7WoLsNFbVZCnlF4f22\n+yrOC3dKwHup68nTbzpdt775ck/9iIbYaInJi5Hr3iHiIyM6dtvBfc/3z17nRl+D0YcIDwAAmB4R\nnheI5NPYuw17h/Drf/xneuHp76soS8FjXeY5c+tdhozsdCxj+/Kk47+Z/1Z3dNwxAW9WiOiqfjpu\npEdEi1QfL3v9a6GuQXLbTmTndrutqlDtNfbxeqUqGvsjwgMAAKZHhOcFbrfbKhpiIzheFdODeEZc\n3KaNGqW7rEBkRq0zX9720ik9E3dzjcSd0eO8pLspJwIGYCw3z7ASVbXXsRTpkJEeFdFZ79TTPnSx\ny36s00bRZQ6Puf7lEXwVeZIRe7NPRKr3RYQHAABMjwjPDkr5JfndQP6arHCykRyT0yLvRrI7BBuB\n2Zr34i2fb++TeXatcnYKG6n+9+qOsXBeuUsC2oVz9My1qcRGctxIT3AurVWuX0MuT3hZcY0tRXbS\n8uFIszpnO1XU4hkRHgAAMD0iPBu4o/FaRr54zavOKkVySsvX9i/aG2LL8pH8nmVpiPx83anw69wt\nAR0GVhKtIj02dyVIdprP8mpUlCeybP76SqBnmo36bEY11y4Y8GywR+KsDf1GBjaK2r/VYKSS+Lxl\n+doyj2W9gdAGJDYDa1uSkWvy4ozegU1l5V/+19n34cvWlNY34BwuC8nNe+GRFgAAmB4RnoCWZN38\nvyOjfO+9kUhOSaTZodvUSzTmUnoaGrZGfrz11ErjEx51AQUdjUW/LOaUkm+wuhbZv3/sax5deuy/\navJq3ueVlDcR19ToNcZem9T60YcIDwAAmB4RnoDWXJBS5ESN8FeN9kZGHcTdwKr8VDX1s6XwXgRn\nwN2HOxWFen/gXCfk9uAKohMUq7LsaOn30/Vi4OSey7JulvqIypiE41+//UH+nr0Izh7XgdYIdfT9\nxdwe8nrCiPAAAIDpEeHJtObqKC05PGrqiK15Jk8VEyoyYyIy6k5INUf0IkURXiNG7y6z5Vxb5Pbg\nkuykmOK3Jae3eaxGR1e9yX+beZWh97u+FqRriYgWjSgpD7fdcKJJKpJdjbKR1xNGhAcAAEzvVhvV\n3m63+/3+rxfuznuEn3U3Zt7Xpjuw591GOOxdRzS6VGp37h3XYx/SHd3Hvqb//v6f//iy7s+fn/bV\neizXMb2DPc7Htj7uQtP6Vu9riMqEq9KSSz4b/7fldvv35X6/b5id8Tiucg2rWV3jbdQl/Q7SNA/m\n9y1///Y6klWGPjjrVmxzQPf3/+0Pj/38epjPv3f1evK4BnfsqzxuE7Fe5Q+Za4tXjaaW+7LJKX6y\nm91uf5XXLyI8AABgepeO8IT7RzjPX2XEIIvaqNF39C5E5dfI6SCyO57HZyxyblZ3FfbvIhJSe249\n8jiWZX1erDwi5EXk1PmQLhXpIcIzK29yUC+XRUZAst+HjQLZCTujv71VVElEekLX2IZ1PB2vyqcp\n5Haq41br8iJY+bqf/p7lX13jetSOCA8AALi0S0Z4opEd1Z9Grc++L5J/E41kRHNcHu///Ll4B1Za\ndvWcOfr3D6VIkMqxieYotUZ48uXUnar7+XkRn0tEeojwzOB+vzdHrt1Itchtya+TrXmQXt7Q43hU\n/lC+fOu2zPtLeUFPx2nzabLlvfw/d/9txVw0z7CyzasiwgMAAC7tkhGeRFUdrZ6/mjwTt9qnUjGk\nqopU1CU6H1ZpX70IR63iYVl0PpFaj9qPyLJuDyCxXiufQyyayyM/C/G9mLsaggjPmZWqNFXuXlLL\nE1mWSmSnEPFQfcXcyk7Rcd5TykMM5yYqIiIkl48ctxdlEpGer5tYf0arz9N8bleN9BDhAQAAl3bp\nTsuq82ZiIwVeNKJpjiYzP5XXYfjrYvGIiJcXk72xvi3n+XQp4pHuWOzx2a7P8pzZyFVwJuZb6W5L\n7NOjK6zY18dyl4js4AxUdLnURf0RFTDrcK8Lwd45j+tnIZLg5keK61ZrZCe/fnhRpOjcYF4n6tXy\neb6U+TzcDvAqmibWV/pMV39THfE7Z3CfCREeAAAwvctEePLcjlUORxpdO1EHVWlkoxfFGW0TMd+L\nmgdGRhWcSNCv3/4g5wKLzjvV+v5SZ2kvcmO3law+Cztze+ncfllgfUdm16UiPeJzld8b5tzCu1Vy\nMB+/EXudsr+dxmuSEo3CLksWHbK5K41zcHnzffW8V+XENEXuzbm31wh1TsPXu3yuRHUtdPbxiojw\nAACA6V0mwlPL7bDREktFdrKVF9dTHMVvqPB6Wrcd3dtnx7//tLqjiXY1TtQs63eRf5SfJ5kX0DD/\n2NO6G9fzsbKPRZ4/L3t3KWeTN5/r1z835GoBL1D6DXuRitYOww8ir+TTn7/Eu5enVdlIT6BrfWkf\nf/vuR52rU3hvaN1On54adX1q7e5vo895TyQvKtYS/boKIjwAAGB6l4nwLEvhTl9EC6LdgW3EJJJ/\nY+8NVI6Ll1lfq5BIr6t1y0qpaPTF3J3YO6r8uL2eH+puSuUo2Yq4mk9Ozo0X6fHOC1Vb2Fu051cp\naqGqd2RX3/hOyX1zq5O8HDzzvkVFZwtRjdbO+Sv29+xVtQaizPL65hG5QKUKM1WNt4qapb87Twdm\nRoQHAABMb9pOyy2VNNG8kdJ8VcvS19lSdUj2nhd7870U53cR0ZPofstZhVU30cDcMnbdq+NzZjiO\nRFfCkTrVkTVYhVWqADwvOi0fifs7N71yHrOMF+aUW3UzdjopuwrXFTVPVW+kY3U9qMwP6PXhSTbn\n6BSue+5xNuY2rY6h8JnZz/zr7pV7mHn9h6LzFR4dnZYBAMClTRvhSbbMWC5n0RZzMiWRjpYjowvm\nD8/7Wlm312coPN9XZG6Zx0vlz6E3yrZa/tsfmj8fta8tM7W3RJ6OjQjPkbhVPZWeYeFqLKfbuReV\nyH8f4fm4nAhQdO7Ax7F89+N67isTFVHXg3DnaXG9+/THz+E5sJrzjMRn8P0//xGef1HNDWgR4QEA\nAJjA9BGeFrWZx0uvq6qtUsTA64FTG8nX9tVdb2V/o7OnR99X21Z01nfvrtNb7/1+d3OUaneJq3Ut\nM0RtWhDheafeea1KUYjVTOTObOE2su3m7JltFyPZIrpge+a4UYhAXx7veFWEOxp1qeUTqR5tXmTH\nm+m8lsNl97/1837sQ2HW+3wfzoYIDwAAuLTp+vCERsTBuZHULOly5FurvLK9K+y61BwqTrfkWrdg\neyfj9V1QfYq+Hl68S7S6S3Rne3f69qjZ5fP12teU1s/bzTPKzslZ747wXt6cenKuqULfKvWbUlbf\nb1sBZnvs2M6+eW8dEaGNVm25c01VougqcqP6hUXzZiI9cbz+Quq4bK6T2yU5q8LzrqHePrTOmXZm\n0w14Qh+eGHx4j0/UP6B2m7UfpX0tUl5e2nf7vuIAyWneZ7VOillrmqguNvZc2gk9vXJ2Lxn60x8/\nx3/ATvKivPjYfb/AhQL76p5yQDVN/dvfZRKvshromGTY8OOZwP5nO/zx5+BUEpX32Ucyj/3yJne2\n67RTNliFpojRwZNKzl6dc3U9fFp1PTHcawLZ+l2bAY+0AADA9E4f4ZHTBlQSTVUkZlRyqts2fSlE\nPAy1T1vCkWo6ChXK9qZaqDVHdEPS9jjSvtkolJMonpTC6VvvTOw+eY8bcq3RMiAkOOVA3piudd3q\ne+815LvdbuHH3va/1TXTjU5n++w+2nGutfZ9MpJVOBaVLiDPmL2umXPeRER6VukQnVOIzIQIDwAA\nmN7pIzy1fBlvGfXfm/clMo2FvQMSy6goi5v8Wzkf3jpsXo3ah9oxrhKmg8ehEiPVHdQr8md6vi89\n30ugmZNo3MPNdam0llhFV0QCsJz82Hu/iFbc73eZyyIbrDqR6mgO4G9/+7ssNpHXKS9S1xqNMfuz\nLLE8oKshwgMAAKY3XePBcLXDsshcj3DzL2/5Wpl2ZdK/p/c5+UWrJoBZu3Gb+e+VVyfelBJyPdn2\n1PN/eRzeNsTEh6V92e3z3PCdOg8aD75CtNFmYEVf1lOZSiZRlZLepJv2e68mq3xqCfHBq+iSEWpx\n7bLbLB3Dar8bm5iqKrWWdhTexNLu1EKBSrjezzPMru8k1zYaDwIAgEs7bYRH3SGpaSA+/vhlGfEM\nd/V200Jcte5OalMTeFECddfkrbt2h2TvUNyJ7IJt7Ff7aiexK2w72uxRTVvRc968SfTU59n6faiJ\nTop4HER4XsmbyNJbTkWM8wktvQi0O3WEIae7+fxZTg6qogWy/4yadDQpXe9tDoszKbBdV+++fPrz\nF318nVNOPK37ywJP+5J/ppHvglo2ovc7+i5EeAAAwKWdvkoreVQUqR44t5vMmF8tIyqBVBWWN0r/\n9T/+M1ThsCy6b4ucmqHWoVjkzXjVZM0dhE2353zbXm8fdRfWW+WQ50t5FRPqOKPfh6T4+Qe7W+Na\nevszeVGZYtWT11HeXh+CUxXI3meFXjheLxs53YO4LtR+T17H4VUVllmX7Lsl/rt2jDKqHpymY1VB\nllacd7Nv+S6YZUv7opSm9zl+pLqMCA8AAJjeNBGeSF+HcA+caI8Eu3xpPiuzzuizXDVp6GpiTDFv\nTF4xoXrYRHv6hKueCttezW/j3HWq87Dah8Uo3fk4vXzcz9OsWy1fXAYoCM+l93WBp/fb64iaJ+q3\n736U32O1rJ3I2O5zpCN7a38d9ftOvHy5pwoxkXOjJuK0ER1vX9R6SvvWcs6WZX09k8sXIniR70Jx\nP+212PkOelH5MyDCAwAApnfaKq1kVc1Uqdqqzf0UWbc3p0ytp4Jb0WUqgBLbn0f1tVlVSmWzhnvH\nu+p1Y6qXZFWGOj+fP7sVYmrf1Dl8vB6ovIpW7u3xffC2ffQKB6q09tU847iqnAp05pU9XcSyq15g\n9nqg+nZl33m3ClNc52QPLPv+SiWp3f/S/hWXFbk6bjVrdh5kFaroYVS6Xufvdz+LQg8gr0tz9Pvw\nUPnuHTmHhyotAABwaafL4fH673hzmuTcHBUni7014/7pb+p5slM5ZdWqnlTujlq3V72klD4Le3zq\nc4jOBv943an2KuUu9H6eLcu7FS2n68eDkaq5GF/e8PR662zbSagqMJjL4802Xsr5kzkronrWu16v\n5tBKlVGFPl9eB3nZR8epqFLX9fw37eULqfya1Weh+qzVrhdbvguFfXhsO53jwvfAy3c6KiI8AABg\neqeL8KyiD14FTWH0KyslbMTGy0ZXuR+VLpsq8tHakdib0XxZ2qMNql9POKpWoO62vKiJVzFWq7hQ\nOUrqTmjI98HLGzjZnRDGsr/X1fde/J69a5Dq2/Lpj5/d/mCrO3kVjfFyRLLf2+o4VZTAvL/UZ+Zp\nW4Hfkd0v+9+rKLpTbSr7FBUiHl53Z1ulaq9v8pw7M7/nat+Fp+MUvHkc8+/LWSu1iPAAAIDpna5K\nK9q/RVU3RdbdOp+N21unktXuVV+1biuvqJB9Zrz5bbYuV9i2V+nlHe8e59rT891JZMVeY4fd16NK\naw/ejNxudZKn8W5+WSpVO+Z1Wa3TsB+q6ij6fqsYCQ/mvXgdmB/vU5VRhQrMahVVjXdtNULr7/gu\nlJar9RLqnZfrFajSAgAAl3b4CE/rrNqPEXLDCNTbRm+FTX5uvd4u0W24/S029OGxr3cvV+jDk3gR\njt5zHjnX0W30zHfkVYjIvkOHi/gQ4dnT6ncqIj1u91uhFAGQFWFi7inVJd3r01KcNdzul5jRW/Wn\nUb/JYi8gp8+OulY2bSM/P9k1LhoNd/ssObk7xeuqd84bv0OraFwhKqlmgT8CIjwAAODSzlOlZbP3\nxd1IrTpL8SqevLmyInNQufsd7P3i7mt2Z+DNiWWPP/p3q3QXoiI70Wqt6DkvzQsW/Xy8c95ViRDo\nVfK07obvKc5LVURF532KqkVbVr19UpTc6QGmKotKFVgqyrBal4lUqOuYvL4VIiqrefvSPtjqM6cq\n07t22WO83W7rPkGiwtNbl/uZZE82ZL+czujg103U880+/f7TASPTMUR4AADA9A6fw5O4c0kFq3pa\ntpWoijA151Rp/heZeyTmipFzzwTnaLp//izn5fKOOzp6r1VcePk+8pm387o7B1d2t2Vfs5+Xqpwa\n8d15xfd0H+TwjBS5Wy7+d7Q6q0b1xFHXMVW9ZK8LlXwbe72y1xyVa+nNb5WMqD57CF5r1fn7uprb\n6lqo5gD0rk1W7d8elQ+1mTruPIfHqTJ8J3J4AADApZ0nh+eDmpPlYeBcRarjpNc1tzT/i5fDk7Tm\nEUWqOpq7/AbzSladPPM5ZsTnEO2RoZ6Jy1yYD5HqtFUn0kq36l6v/J7iBGxuhr2m7NC5Vt6hq8hH\nuraorvWPt5XzcJZlfXyqg/AqJ8fpyKz6WrX0CFLLeNdaWXFamrFcdK2PdkyO5t389t2POnK3NdLT\n8l09WQ4iER4AADC90+TwJLX9zbV0x/X6sSQqt0X1dci3s8rZsXcN4m6i1u2y9P7iHUJjnxmVZ+L2\nKSqQ/Te8DrOd5+fpebo3J4zTcXXLDOcjv6evRQ7PSG5nYadjfFRxfqdgXxaVeygjBiLHo/T7WP0O\nxO/Y7ciu8muy5VfVYzaqIo5fRWVqXezzbefkOrx8G9V/x0bIC/2VvHzIpk7ZpX0qfFfVd+gIajk8\npx3wqAnsag3t3IGN07RQ/WMspxGoDD7CSXpew8VAC/poIzGvvN5N6ivtQzTpeMS2Pt7nTY0RHQi5\nYefKd673e/p+DHhGUt8DNXWCN+DxyrxL0x08iN+9miRYTu9QedQjb4oCjVLzffm6KfGbLPwj7p5T\n1RTQSbyVN2HZMfcer6IGgPm/VeoaKBsHdg6ESuf1rAMeHmkBAIDpnS5pOZo4XBpprxJ/VXKeiHrZ\nJK6uffSaRYk7mXDSc2kCT5HUJqflUHeZKhGvsP7mpGN7nOr8OMmNRSYq5rZF9+4QC48AZYPIw0Zy\n8E6r5piNE3g+ohEi8b54jXIe4a/fHtvmU0sItR+2gEBcS2XT0GDS75fdKEeRV79rp+mjah5Yum6q\nR1fq35jWqHLLVCPhR/rOv0FJ9Lt6BkR4AADA9E6Xw5NEm+TVGrupJlmymZ+TgGjV9k0mBjvPz73X\nixN4ikiM1xzQrvPxPmcCxFppePQ4vGfYtWf9XuO06J2t3ReV3Bjdr9o2j4McnpG8O3OZSBstMfaa\n51W2Wcv/ybmT7Baa57mNRb1k7WDTv+K2nXxA1TjRTSiu5DaqJq/evzHh3K5CRLyWx/j03rSOYCNG\ndR5quank8AAAABzE6XJ4EtU0Ljph5sdKnv5TNvNzJoJLVF7Kr9/+sNoPGwnwcj5UmaLMQ7nd3FLu\npLWi6PH8XdwJ5OtX+6cmDXy8HpzotLTv3nNxNWngqkmiOR+REnJv4lIg5/2u3Qlw7feq8B3tzROM\nTuT7OJas4ah7jRRNEFd5hqL5XSkCYq/P9ngsLydT5iFW8qVkw8UPq2tTdALjQv6RzL0R0ebod2n1\nb1FD/tDREeEBAADTO20OjxWZlNHNwWlsiuX1ksjPrcrVCVdKOI25Vu/PKqXsPpTeuyy6EsLtU1Ho\nY9Q68ahsOBY8X8VzHfx83MZiDTlAx58c1EMOz0gt1TXLshQb6tVeb6n28fJF3Il5jWK+iRNV9tYt\nJ2C2CtduVY1a691TXae3j9l56+2zY7ct+62VztvWfnJerlJDRIccHgAAgIOYJsJjle543A664vVo\nFKJ2F+9FU9zIjTN9RWl7an+6u78GuwSHti2eG3v7Go06ldbh5f+o6g3vDir/bh2/CstDhGek5ghP\n0jpNQKnCxqvgaowmrfYh0t1ZrMudakFY5Whm183miG7jZJuyr1nHdD7Nn2thW3LaCa8r/egpKBYi\nPAAAAIdx2iotT2Qqe3U3sspuD066qSqO8k684U6aNpqS9qkSkbNUl89VhYCovgi/r2eSTacPkZz3\nx1SIlc65nM/Gq0J5bOT5XHsduW/Z/F3AEM71INTB2/n+rqqPRNWP1939KW9QzfVlowZONMGr0ixV\neXoVXfY4ZWWs2LdQbyOzDtVx2u2Y71RIlSbwtNt+nA/nuzJD9VUUER4AADC9aXN4SrzM99ZnmF4X\n4FrFlDfPSaLyTiJVX/aZ/apTZk9lQMaur9ZpVVVVed2eVcWVmoW4FOmR50pxOmiftwIrghyekbpz\neDyN3cJLovk2qvJq9ffff/LzW5zfltf9uTYLubrGyNxMJwLs7mP+74SXo+Sdu2gl2Yfv//kP9zMO\n91sbgBweAACAg7hMhKeUR9N996HmRRG5Pfm8Vioy4eXDuNsofI4tEZl83bU5Y57eV4kYyUiNl18j\ncni8u7Q8Uhbdhny2Ha2YmKYyK0eEZ6TRd9Vep/Xq9pyqLNm5V1X9FOa7WkWs7TXDq4wSfYbs8SX5\nemWlp1N1KecK9PYxOx82L8idp8s7p07E59Ofv7gRunDftI6qLIsIDwAAwEFMW6VVfB5rRvTqjsaL\nRnjz3li3b77R86+ofdIHVt5GbQ4dsZ8qmrKap8xWeXhVDmJ/asfhHn/lzs5uT30eahurSJDZtLdP\nefRwrmgP3k3OrdcQnY5U/BTXaV5X83vllZPR/LjVts08UN7xtUR2VWWnN++VtdrX7FhanxZ459SL\ndD9VxNlITXZdqu2bmittRMTnqIjwAACA6U2fw1Oc70TMieTl1aiqrJa7e/V82J1LqrUzcTZ7cHRf\n1FxSNudl6LaD83R50Shvf0rbCM+l9aG2D/NUbJHDM1JvDo/MdQl2P47MpbXKO4lWrVZ+g+qa8nXR\ncm6P3aeWaqW076oySuYJCm4uU6my1un1k0TnsbKK5y04l9ambt1B5PAAAAAcxOlzeFQEpHRXv+o8\n6XXSjW5TPBvOIwKr58mtuR7BCEKef2OPy0Y4bGdSe+fj3q0EuyOLHU0riR2PulMs7IPqhaE6Ya+2\nle5w7HE5FTL5Nuau5MJobr6dmoPPdGJ/+u7aXA0RNfK+s17U5SkHxsm1WeUwCo/ohJM/l1/jWnMQ\n1Tq9+a6S/Fh6+w/JHK3AeUv/PxoFv4vIj3p6MGNuDxEeAAAwvdPm8Hi5LU0zmDs5Kl7HYW+W8U9/\n/uJGZiK9fJbFz3nJ19c6w7j6LsjITsfM79HPrTUykj/bbp31PdqPI/KcetXdufFzez9yeEby8kZU\n5Y9XOfWg+nUF+vAkNkfR+92o5T/9+YuMBjzW7fWnMWxeXaSnltc/TPVPi1arlXJj5DlSvdu8fFLx\nGeTLt+Q31Y7rwavirXxW5PAAAAAcxGlzeOwzbhVBqc6mLUa8dhk1e7rKAbLPvp+qGLwIhu2hYJ8n\nqx4LhWfnqzsSkcsS7dcgIzvmjufXb39we/3UnoeXXvfOW54bJc+Nk7vjzaWjcoBqfXhsnhTwxF63\nRA8gNp8AABZQSURBVLWP/PtjsfV3V85QLn4X3vffm/evNGdgaVbz0rpUPomXJ5lv267bHs/X01CP\nUK+2bfuOFbat8qNUFGaVP/nxPtn7raFnkDzn3ndJ/TuQPufTV6AS4QEAABdwughPNBphR+N5Tks0\nW19u28niDz1Hj1YQiE7MbofOJf6c3HLnu7HZ/oX1q26usqOyPU57R6POm5VVa9h1P/bNyw9yOnKX\nInp2m9HvKa7J+x170ZhoVLK27WQVsXGuOattZr8PFYFS11QVhVhVTFb6C9n1y75C5nW1bnWNUpHx\n5X6XEZvVtcM+PVBVu7YTfaHC2I0eqerUxjyx0nf1rBVbp09atiJJyla4nE8l2jpJcWYnvrzX/oDN\n32XymhPyLX4RVSKdM5met+1IuaJK9FNJiO62vAtfvg6RjO4lErcmFPZ8547boJCk5ZHUwNdr8hlW\nuWbJKSSc7/WqEacqsS40+JMFAOr3LZoEWuo3WZrAUzZOdRLEw8UZhetm8/E6jQdVIvlT+w2xrlWD\nXG8yVEfpvKrCnSMgaRkAAFzaaSI8raV1LY8MZORHRCHCkZ/sdTciU7lretpXMf3FY58L58crt4+W\nhEfLt3OyHNWLogXPT63BnxvJcR51tURy7Dr3+J6+BhGekbzWF7KNwdZHBoUIgIrYhCM5NnIifsvL\n4j/S9UrjvfWsJgDOGi16kQ8vgqu2LZevrOOxLqccPzqVSH4e7OfmpiI0qn1Xe1p2vAoRHgAAcGmn\nSVqWya4D122pUkhVQi2nO8he88ox7V1T6+SZpaQ2WTKtIhadDQhX+5AvaxLpVBNAdXemzpvd51+/\n/WGVnOeV+quEz548mz2/p5iHe03Z6n53pxDwmv0pq99ydn2RCc3CagoF1eKjUpzx4JRPq0KH6LVW\nlnln25YtP5zcQzXtkfyMssTh0ZEdq/RdPWubDSI8AABgeoeP8ETvytVkaz25PKrpU/bG2L6Wmh2q\n5+DeJHLidXWcv/3t780j/63RiXx7qlmhaoIVbpIVmODQvVsWJfDJiO/Ont9TnEd0EtBwTkfQ0zQP\nXnRB/O5VHpqKWpQqw2qT/C5LISfPuy6I81IrlZbL2ONVjfhs49ZCFOrxL4Lab/H5Jl7zWuv2zTfu\nuev+7gS+q9EI3tEQ4QEAANM7fJWWzJT3esaIrP/qNsToO9qnJzJxqVuV4Uxs6e5r9veWiVS3KB3T\nqldFa8VU4zmv7k/rOe+Y8PMV39PXoEprT7Jap6Hqsubp7tzrK2b77Tg9gSL9rGS/HNUTRx134Pr2\ncTDP28uPx5vQM3iNcius/vzFryIL9nBbHYP4TPLrRaRHUQt3otfs6cER+4lRpQUAAC7t8BGexO04\nHKxiimzD65rprbP0vNqLEvRuIyl1A1XnRk4aqno+tC733Y/VrqQ9x6fe33Ouo9voiYy5d7hOb6f3\nI8Kzh+jEu7VKzwjZUyfnRQBURCQSKRDrrvawWXREQ/b8Kl1XgjlLrdvw/o3JX2vOvYqe646oTei7\nUCA7NWeRnpbo96sR4QEAAJd2+CqtZNVvJjCJ3LLEqmC8DsNe/xn1/loGu1fV41U5yQn/sknsopNf\nqskEu5fLPxsRRVHHpc6L+hx7zrU9h9H319avcg68irDjRHawp+iEld51QWma4FH0q5G9bkSUsrSc\n159FTpZp9+2D15enFgmTvb6cCinVX82ddHVZ9CSi6tzZvmSGmv+rxp2YVi0nrrWrvkvZ04OzIcID\nAACmd5oITyLzR4J3DE/rEP12wnf4wX48pQ6kdpteBMD+PdLRNNrbQUUZHn93zrG6k8r3e3XXEDxe\n+9/eZ5P3AFpp+LxatpmvOxodO+Kzb+xH9a6JVl8qMpIQ6MO1igConmBi32tRB9lB+evGl2Xx561z\no8zZefKiKs3/dgil+cHcjtkqmhY954F9rH0XSq9bNpJTi/REo99HQ4QHAABM7zRVWpac4byhWsur\nkIm+LredPfN0ez2Iu4/W6q5SVCmJ5qyofKLoPpSWjZ5LtzLM68+R3X14PY3UPvS8Hu2nlBw3d4cq\nrT3J2dCDPXOsWiWOV6WjKqMSrwdM6VhkD5doFVLw+EvRCtv76nEc6rosfquJN3P907yFXh8lEdFW\nvZBkDyDRI+lpHR3flWWpVGcVPiv68AAAABzU6XJ4LDmnkpHP8OpFUXr708hn29n8TuEqg4+/N8/R\nlD1/jR6v3ab878ef4314vFmhveomdd6S0vP0RJ7j4OfZcrzq+9da8YW5ebNiq+/z6vcivkf5++Q8\nXiJfRFZ+mvWoPJV8vbZaKfFmcJc5TWp+q2w9XhS4dd6uaMXV93/+IiMeKm/G+ywesn9D8vXnVXiR\n74JdtnQ8ajb5x/ryz/eAkZ0IIjwAAGB6p4/wrCIhla6Sbub/1zc+vy+6fC3r38nhUHdhqppJRWOe\numEGZ7S1x+X1tlHnoZhHY4m7Ru/uw25b5XDdsufLXjXG1u9DfkxyGZO7gGuTFYGdkb/a9UJWDIll\nPat+LIVtRztE20iXvR6u+haJObTyKIyc3duJorizyaveQaXrhYkSe1GiyPUsf3/tM/X+7VDLur2R\nCts5a6SaCA8AAJje+SM8HyJ3K713V171knpWmnz68xc3emD3xetI7HbyvN1W0ZTVefDyBcTrq27P\nX1f89L7ifnodpMXdRlPUxenK7X6ewe9D9f2dcyFhbls7bnvRiqe7eKdTsMrdsd9Zr9txvrycNdz8\n3ptz+5zf0+2bb8JdrBO1Lm9fiscojk9Feh7bEnkzq87yhVyepu+CWfax35nwd/CkXZaXhQgPAAC4\ngNP24Uncfjw10aqcD6s+Bk6vlWKnZXH3YHtIRPvY2L/nfRu8GcttDwhVAWHvXtS+luZasXdX3kz0\ncm6thvMmP4/Gz9PuY8936jz9dxL68LxCb9+t1Xo29Epx+8yICqNVv5bst+f227HrznIOq//tRBV+\n+/aHcJ+d1b8ZhfzH0H/nxyZy9tSs4i39hUrrD/UCa1i2ZNR39NXowwMAAC7t9BEepXZclttJWUU+\ngsvnr6tRuOxy6d0hVPrxqGfZ3jZU1CW6ntK2VR8adRwyr8C5W7nf77t/nhHHj+QoRHheafWddGa0\n9hQjBF5unlqX6Mxrr1XJ/fPn9bXEud7VItT5PrvXg0JVqooKu52VO3KAbD6Me82MPkVQStWohjd3\nlmtjvtm7EOEBAACXdvoqLVntM2AUqqqQwvNBPa/saf+is2nL3hBOH5vI/qrZcb2eEerY8t4Y1f2q\nHEcS6m20iCoHcQfX+nmqfY2gwzIiVt/JTqWZsR939o09oGQ/rkCl6eNaImY1lzOXC95s8o/K2Oya\n43YgFrOB2+uYV8X6WN8fP7tzZjX3evOiM5XPtPRdqK5Labw+ngERHgAAML3TR3i8CEJu66zg4X0p\n9Eewo2t5ZyfmdfEiBuqO6nnVTu8b0dXU6wlU2k501nO7DjWnmFfd1duptmbL96Xlewm0kpGBQqVk\nbw7H6hqk3pj9FuVcYc5s36pfj9cz7Osu3GUV1eo3aCI57txgdr4zez3429/l5yHz/kQPJK87do2K\n7Hid8a/k9AOexGuelSd5rRowqRBnUHSCz9J7ZfM69QNwwtPVgU603bv3CMv5cT5N7+CEZOUkgeoY\n1EXsQ14aO/rzlPuen1fRnBGo8aZzUeRExnnhQHCdpcKHZSlM4KuaCRamWFhdt5zfg91nr0lecQBl\nH02pKReCj5PktD5mO6v9KPAmF1aDtdJ1dLW/oghDpktc8DE7j7QAAMD0LlWWPqoJnldiaEsua6+1\nll+3lIyrbSS90Qe1nmoZvih9X5WjeqWjojQ0cs694+hu9lj5rp0PZenv5F0HohGE3777UTbvU+t4\n/IZEeXYiy6ArEQMvqddbt0p+zo9JNjO05erOVBHW6tpSeCRUuv6o9+bHsyrfbzjnq+Np/Lzld+sk\nDQYVytIBAMClTRvhaeFN55C4UxBUohThiI65K1HRCbvv1RwmcXekEomb31fIl1KRmWhJf7hZWOkz\ncqJjPVODXAcRniNobUi4anz37Q+rJnarCE60+Wlw26XosspN8SJXKlpUawK4ajiojt+L0Npz7u3r\nHz/LBrGPVXrnMnrNStvMtuMeb+O2v/75nJcAIjwAAODSpo3wtDR+U5Nphp87O5Gh2kjZjr7VXYi3\nz9nGvuxr1mo9Uc/oZV6Nky/0+Hvpjsd5Zq2oqFrpLjKyfL7fq88neCcXibLNEw0iwnMkXoWlzVvJ\nv+PedA0ymtoov2Z5EevHfpvfs3fNdKOznz+7k2Ym0VwVmatYiORHJyyNTuuxOoZCPpLXPiSRUTbD\nu86dBREeAABwadNGeBIvUlJ6b6KiC96El5FtrKIOzl1YNIclud1u4UhG9FmtylEqPfut7Ve+37Ia\nRUWTOiIp7kSsnVG2p3VM04adCM+RyBwOEZXJK3dkdMGJvkSV8uxUHkjzJKnRnjgfqpETlasXbIro\n7duXPznHufWcV5a31yuZY+nsAxEeAACACUzTaVmp5s84eT6qWklOeNnS2dfppOx1Xo1UHKm7omgl\nwKprsOnEbO8QSudR7Z/bWVZVyAXIbtbmPNztHZ6aoDTwuZ4/soMjik4LEI5OLIV+LZ1TDqymkci4\nvV9EZ3k54WngeuCtU06/43WvV+ttmSS6U22KDq+Lvaq6be3APRMiPAAAYHrT5/AkpUoa1SF5tayX\nA+JVeeWcngfh6qyGOaXC6za5LF5llOyW/Le/u8/Lo9VazTkA+Txe4nON5mB5HbTnqczKkcNzZCoa\nW+254uWPOP2oFDdCXOHlnXgdiktzTq1ycVrnpxKRH1XNGjrextxLpTg3pJMPVOrNlJslZ8cihwcA\nAFza9Dk8ST6Dd/63Zfk6orf5NKscEDN78OpOIpKfEqxOcqMGTlfgT3/8LCMzT7MaF/Yh+n67j3mO\nj3fnpoQrDQL5NN7nqnKw1Oeq1g8cRvabl/kfIidF5bi4uX35bzKYByQ7MXtRkxT5LeUPibyfWq5R\n6f2qqmmVb1kRzr1MnHmtSp+Zl4NVm+vvqojwAACA6V0mwrMslRwNczdyEyN7G+lRdyO1qh471l7d\nLXzsk8oTsdEjb1+LxxXMOWl9f07lx9h1eZEgG02xdy/W/X6XlW9ebx/1WaioG5VZeLWW3+TjDj/9\nQeXwOZVgq5wXe43KohGr6iRxjXVn+HYiRKtobCUy1PLe3GrfKtd99XlEu/Wrmd2T1b9dy7L6PFUc\nZ8t1fDZEeAAAwPQuU6WVc7PsRdWCihB9XSxWDVVa1psXxYtOlSosvFnBo1Vr0ffn22mdebxW8VXa\nZuTcts7T89jX4PdiTlRpzaA4t5Tl5Y2oCIfqtJ5Vwq624cyp5UZCVP+hQkWsqpL1/t6zrbSv4Yov\n1T8peI4jHaVbO+jPhiotAABwaZeM8CTFnhUlTi+FLRVXXi8gWbXkRITyPjyWnD1X3Y2JO75arx05\nX5V4Vu+d28iM5fa4o/OQhZ/pB2dsPzciPLNYXdvttSQ4Y/nqt1uZGdzr5RXtpxXu02OuJ9Vt2fe2\n9tmpzR0ojjuRc6GZfQp/Ft/9KHNy5r4++YjwAACAS7t0hCfxIj2lWYGXRXcmrXUeXm072u1Z5KXU\nugNXOz5n21J3J7ZzdBLpITHyOPJ9VevL7wC9/hOts0ZfI7KTEOGZ3ep65+TyPK5z4jqZXx/C/WUc\n+azv+fKr60TlGhvuqK6izw2zpnu9irxznsinBYW/X+N61I4IDwAAuDQiPJnw8+cP0RH2/X4v5tgs\nS+EOIJjjEtlmsorUiGfaai4wdbe16lOTPXdvOTeldXs9c9TdXGS7kefjy3K1yE5ChGcW0Rw1r/dN\nrTrpablCN/to5+UVFQGpVIrK/Mdo1Wk0p7Owr+5xe/mRTlfrahT6EtWjcUR4AADApV2q07LHzrli\n7+yboxaFDqTZm5ZlKczPIjoM95CRKrMPsnuz2OfHeRBzVrXcacjjDPbGCZ1rsc3V353PH5hJNLKj\n1Oaoapk5vUj10lLXzUVHi1evO322evZV5T1F5+9SHeVlND7/zJgrK4wIDwAAmB4RnoJoV2Nv+cjc\nJd5cU5uiDCKvZTWbuDdLsnc8af0b7jTsPq6iTeJutGeeGO/zJLKDGXiR2miuSjRaszmqU6CiMtW5\np5yoif3vllnQAzv8ZZ3mmqoqehN3H7wZ7xFChAcAAEyPCE9Aaz5Na0RoWfQdQa/b7db9DL412jRy\nNl6ve7Xnt+9+jEfgRtzRAQdXnGm7ovV3/PT7763KElRUprR+GwVS+ZGrPkKVWdB7NV8LvVwe8T60\nYcDToPlRV8cjnvRFr03M2UolE0cHZu70Dx2l897xeQmVlRWH94+LBq4o+qir54ZAPnLpHQil37N9\n5B25Pojrr2ok26v0OG1rOxEeXe2DR1oAAGB6RHg22PPRiJqEriXyY/dPRTzU/m9dPrK/thniyARC\nHl0BmnzUtaXMWZSTb438qBYbkWkgtiybq+37IynZvNaNR1e7IMIDAACmR4RnAFn2XYu6BBtSJV6J\neC1fZVXybSIe3l1E6/L3+30dBbKRHFEKr+6MvPMWOecAtF2KD8TEnTLyoyI+zhQ0zs50Lav26XFt\nzaZ9GBWZHvkZYI0IDwAAmB4Rnh3ldzMqa18+X1YjfBv5ERN6lra5paqqtnzxbi7bj+J+muOR01uI\naSvUvhDNAbZRTUAfTL5d6TriRnbS66aBoIoI26kWujjLqmvuIwr1sa/2uG/ffOOWtq+Ou3P6G2xD\nhAcAAEyPCM8L3G43v2W4aLSn7ghCFUjRKEvQLXtmvSy6sVdtP1cRLFGd9cjx8faFCixgV9Fqrvw6\nl641bmTHTIopK0FtxGdDk0AvyrLatt3XUqTHi4olVF+9FREeAAAwPSI8L9JSyfXEydmJRG1UlKXX\nY0qKQHRFRZdU7lFrlQJ3SsBr2d9o/hu31wQ3sqNyeFTH+RGCXd5XlWSVSI+6Ftp8H6qv3osIDwAA\nmN5NTVe/LMtyu93u9/u/Xrg7sO4m8qH+O0l3Ld//8x+r975qX+1+5K95x0HE5t3+bbnd/n253+9T\nfBBcw17nfr9//T1//rwsix8dsTk8ydCITisT8Ykciz0Ormvvc7v9VV6/iPAAAIDpEeE5GW9uqqPc\nUajI05ZZ3/EKRHgwjhvZTdGT1lnUX0nkQObHcpTrLojwAACAiyPCc1L2czv6ncXZ9ve6iPDg9Wr/\nDh0F16xzIMIDAAAujT48J3W2u42z7S+A1+H6gFcgwgMAAKbHgAcAAEyPAQ8AAJgeAx4AADA9BjwA\nAGB6DHgAAMD0GPAAAIDpMeABAADTY8ADAACmx4AHAABMjwEPAACYHgMeAAAwPQY8AABgegx4AADA\n9BjwAACA6THgAQAA02PAAwAApseABwAATI8BDwAAmB4DHgAAMD0GPAAAYHoMeAAAwPQY8AAAgOkx\n4AEAANNjwAMAAKbHgAcAAEyPAQ8AAJgeAx4AADA9BjwAAGB6DHgAAMD0GPAAAIDp/cV/y3/dfy8A\nHMR/efcO7IBrGIBlud3vd/3i7aZfBDCt+/1+e/c+jMA1DLgedf2qDngAAABmQA4PAACYHgMeAAAw\nPQY8AABgegx4AADA9BjwAACA6f1/AEH4UKCKaJ0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f708e1b3790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_four(pile)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bigger sand piles\n",
    "\n",
    "Wesley Pegden at CMU has studied the single source sand pile model and the fractals it produces.  On [this web page](http://math.cmu.edu/~wes/sandgallery.html) you can explore results he generated from sand piles with a large number of grains in the initial tower.  I'll use the images he produced to estimate the dimension of these fractals."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`read_pile` reads the images Prof Pegden generated and makes a `SandPile` object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.ndimage import imread\n",
    "\n",
    "def read_pile(k):\n",
    "    \"\"\"Reads an image of a single souce sand pile model.\n",
    "    \n",
    "    Images generated by Wesley Pegden,\n",
    "    available from http://math.cmu.edu/~wes/piles/\n",
    "    \"\"\"\n",
    "    filename = 's%dmono.png' % k\n",
    "    array = imread(filename, mode='L')\n",
    "    n, m = array.shape\n",
    "    \n",
    "    # select the lower-right quadrant\n",
    "    array = array[n//2:, m//2:]\n",
    "    \n",
    "    # set the top row to an invalid value\n",
    "    # to avoid double-counting\n",
    "    array[0, 1:] = 17\n",
    "    \n",
    "    pile = SandPile(1)\n",
    "    pile.array = array\n",
    "    return pile"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's an example with `2**20` grains."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(410, 410)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k_pile = read_pile(20)\n",
    "k_pile.array.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the four patterns look like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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w3v8MDU8+KwUAwy56nrc3pqlz3A7NR/YJAIH14SE1hgQIZcxzsYYFFhFbOpj6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0oQTe0B/QEb7T22RkWyGDDnOV/Q2Q2KuzsfEDPx89z6aTZA/Bl8+31l/KDPwnY28mCEmC1C2a6B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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f708ddc51d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "viewer = SandPileViewer(k_pile)\n",
    "\n",
    "vals = [0, 85, 170, 255]\n",
    "draw_four(k_pile, vals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating dimensions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`radial_box_count` applies a radial version of the box counting algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.stats import linregress\n",
    "\n",
    "def radial_box_count(pile, val, plot=False):\n",
    "    \"\"\"Estimates the fractal dimension of an array.\n",
    "    \n",
    "    pile: SandPile\n",
    "    val: value to count\n",
    "    plot: boolean, whether to plot cumulative sum vs distance\n",
    "    \n",
    "    returns: estimated dimension\n",
    "    \"\"\"\n",
    "    a = pile.array==val\n",
    "    n, m = a.shape\n",
    "    \n",
    "    # for each non-zero cell, compute the disance from the origin\n",
    "    indices = np.array(np.nonzero(a))\n",
    "    distances = np.sum(indices**2, axis=0)**0.5\n",
    "    \n",
    "    # for each distance, x, compute the number of cells with distance\n",
    "    # not greater than x\n",
    "    xs, counts = np.unique(distances, return_counts=True)\n",
    "    ys = np.cumsum(counts)\n",
    "\n",
    "    # select only the range where the cell count is greater than zero\n",
    "    # and we're still inside the perimeter circle\n",
    "    r = min(n, m) - 1.1\n",
    "    legit = np.where((xs>0) & (xs<r))\n",
    "    xs = xs[legit]\n",
    "    ys = ys[legit]\n",
    "\n",
    "    # compute the area of a circle with radius x, for comparison\n",
    "    d2 = [np.pi*x**2 for x in xs]\n",
    "    \n",
    "    if plot:\n",
    "        thinkplot.plot(xs, d2, label='d=2')\n",
    "        thinkplot.plot(xs, ys, label='sand pile')\n",
    "        thinkplot.config(xlabel='distance', xscale='log',\n",
    "                         ylabel='number of cells', yscale='log',\n",
    "                         loc='upper left')\n",
    "    \n",
    "    # fit a curve to the line and return the slope\n",
    "    params = linregress(np.log(xs), np.log(ys))\n",
    "    return params[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following plots show cell counts versus distance for each of the 4 values, along with the estimated fractal dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.169"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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5h9Tm3Dm6J9ntWzkYWfywpGGMx3mhugBYV3iQZ+ZtC+qOGpjVhp9dmUNKc/tRFi32J22M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\nEzJLGsYYY0JmScMYY0zI/j+RU/0cQIc/ggAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f708dca18d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "radial_box_count(k_pile, 0, plot=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.828"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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uS4+lpGfXJPVKJLHaNTxlZvPd/ZQ49Cfa82t4KgGULppVbd/Lfa8sjnhQL8vg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\n/j8/WzGyv0PFKAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f708c1ebc10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "radial_box_count(k_pile, 85, plot=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.355"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gnDjVUCQ2ggSNYnefEoV7DwWq2mxvpjmQ4O4zgBlRuKeEKLsIpqGxiRcWVvPO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\nChoiIhLY/w8SlByhA0qXeAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f708de681d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "radial_box_count(k_pile, 170, plot=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.519"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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i74GmE/VO6NuVW8cPpktHLQMirZcy+2mY2TTg68CWxnuLm9nFwL2EKphp7n7P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\niZqShoiIRE1JQ0REoqakISIiUfv/AdH5IwNqrY6iAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f708dd856d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "radial_box_count(k_pile, 255, plot=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`estimate_four_radial` calls `radial_box_count` for each value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def estimate_four_radial(pile, vals=range(4)):\n",
    "    dims = [radial_box_count(pile, val) for val in vals]\n",
    "    return dims"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here are the four dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2.169, 1.828, 1.355, 2.519]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimate_four_radial(k_pile, vals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It sure looks like they are fractals, although the dimensions greater than 2 are surprising.\n",
    "\n",
    "Let's see what happens as we increase the size of the pile.\n",
    "\n",
    "`process_pile` takes a value of `k`, reads the results of the sand pile with `2**k` grains, and estimates the dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def process_pile(k):\n",
    "    \"\"\"Read an image and estimates dimensions.\n",
    "    \n",
    "    k: reads results starting with 2^k grains\n",
    "    \n",
    "    returns: list of 4 dimensions\n",
    "    \"\"\"\n",
    "    pile = read_pile(k)\n",
    "    vals = [0, 85, 170, 255]\n",
    "    dims = estimate_four_radial(pile, vals)\n",
    "    return np.array(dims)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here are the results for a range of values of `k`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 [ 1.7308  1.563   2.6762  0.7751]\n",
      "11 [ 1.8127  1.8163  2.2902  1.3133]\n",
      "12 [ 1.9158  1.9331  1.763   1.4415]\n",
      "13 [ 2.0721  1.7016  1.7659  2.3933]\n",
      "14 [ 2.1234  1.8487  1.4476  2.5505]\n",
      "15 [ 2.1317  1.7756  1.6045  2.5421]\n",
      "16 [ 2.0606  1.8966  1.6208  2.4119]\n",
      "17 [ 2.1201  1.8799  1.5338  2.4595]\n",
      "18 [ 2.1748  1.855   1.4378  2.6163]\n",
      "19 [ 2.1587  1.8538  1.4463  2.4759]\n",
      "20 [ 2.1693  1.8277  1.3545  2.5192]\n",
      "21 [ 2.1785  1.7928  1.3467  2.5405]\n",
      "22 [ 2.1931  1.7649  1.3339  2.5081]\n",
      "23 [ 2.1833  1.7624  1.3153  2.4947]\n",
      "24 [ 2.1733  1.7665  1.306   2.4709]\n",
      "25 [ 2.1642  1.7615  1.3142  2.4436]\n"
     ]
    }
   ],
   "source": [
    "np.set_printoptions(precision=4)\n",
    "\n",
    "ks = range(10, 26)\n",
    "for k in ks:\n",
    "    dims = process_pile(k)\n",
    "    print(k, dims)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above `k=14` the estimates are pretty stable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "res = [process_pile(k) for k in range(10, 26)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+zJub32T2+NlcP+76sLZQ2pPa8KgfHLsO7eKHkh/YUrgFp9vJ0IyhDM0YyrCM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\nmzkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f708c1ebd90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lines = np.array(res)\n",
    "plt.plot(ks, lines)\n",
    "plt.xlabel('k')\n",
    "plt.ylabel('fractal dimension');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Might be interesting to try a few more to see if those trends are going anywhere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
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